ABSTRACT. We consider a monopolist selling n items to a single additive buyer, where the buyer's values for the items are drawn according to independent distributions F_1,F_2,...,F_n that possibly have unbounded support. It is well known that - unlike in the single item case - the revenue-optimal auction may be complex, sometimes requiring a continuum of menu entries. It is also known that simple auctions can extract a constant fraction of the optimal revenue. Nonetheless, the question of the possibility to extract an arbitrarily high fraction of the optimal revenue via a finite menu size remained open. In this paper, we give an affirmative answer to this open question, showing that for every n and for every ε>0, there exists a complexity bound C=C(n,ε) such that auctions of menu size at most C suffice for attaining a (1-ε) fraction of the optimal revenue. We prove upper and lower bounds on C(n,ε).

ABSTRACT. In the private values single object auction model, we construct a satisfactory mechanism - a symmetric, dominant strategy incentive compatible, and budget-balanced mechanism. Our mechanism allocates the object to the highest valued agent with at least 99% probability provided there are at least 14 agents. It is also ex-post individually rational. We also show that this mechanism is optimal in a restricted class of satisfactory ranking mechanisms. Our mechanism coincides with the well-known mechanism of Green and Laont when there are no more than 8 agents, and modies it for higher number of agents.

ABSTRACT. This talk has been cancelled.

ABSTRACT. This paper analyzes a bilateral trade model where the buyer can choose any cumulative distribution function (CDF) supported on [0; 1], which then determines her valuation. The seller, after observing the buyerís choice of the CDF but not its realization, gives a takeit-or-leave-it offer to the buyer. We characterize the unique equilibrium outcome of this game and show that in this outcome, the price and the payoffs of both the buyer and the seller are equal to 1/e. The equilibrium CDF of the buyer generates a unit-elastic demand on [1/e; 1].

ABSTRACT. This paper studies the price-setting behavior of a monopoly facing two capacity constraints: one on the number of consumers it can serve, the other on the total amount of products it can sell. Facing two consumer groups that differ in their demands and the distribution of their willingness-to-pay, the monopoly's optimal non-linear pricing strategy consists of offering one or two price-quantity bundles. The characterization of the firm's optimal pricing as a function of its two capacities reveals a rich structure that also gives rise to some surprising results. In particular, I show that prices are non-monotonic in capacity levels. Moreover, there always exists a range of parameters in which weakening one of the capacity constraints decreases consumer surplus. In the long run, when the firm can choose how much capacity to build, prices and consumer surplus are monotonic in capacity costs.

ABSTRACT. We analyze a model in which the consumer's flow utility depends on past and current consumption, and the utility function is either strictly submodular or strictly supermodular. Suppliers are small, so that each interacts with the consumer only at one date, but search frictions give rise to monopoly power, and firms offer non-linear prices. Consumers have identical preferences so that differences in taste only arise due to differences in past consumption. When firms observe past consumption, they induce excessive (resp. insufficient) consumption when utility is submodular (resp. supermodular). If past consumption is unobservable to the firm, a pure strategy equilibrium fails to exist. In the two-period version of the model, we prove the existence and uniqueness of a mixed strategy equilibrium that gives rise to a distribution of period-one consumptions. Consumers are better off when past consumption is unobservable. We also present some results for the infinite horizon model.

ABSTRACT. We investigate a two-part tariff licensing contract that enables an incumbent innovator to license the technology for a new product to a potential rival, who may alternatively develop a compatible technology for an imperfectly substitutable product. We identify the optimal two-part tariff licensing contract based on the development cost incurred by the rival, the market parameter, and the substitution coefficient.

ABSTRACT. We solve the revenue maximization problem of a monopolist selling substitute products. We consider a Hotelling model with two horizontally differentiated goods located at the segment endpoints. Consumers are uniformly distributed and their valuations for each good are equal to base-consumption value minus distance costs. We consider different distance cost functions: linear, concave, and convex. When base-consumption value is high, the seller maximizes her expected profit by offering a menu of base and opaque goods. A continuum of type-specific opaque goods is optimal under convex costs, whereas a single half-half lottery over base goods is optimal under concave and linear costs. When base-consumption value is low, only base goods are sold. When base-consumption value is intermediate, the optimal mechanism may entail lotteries with positive probability of no delivery. Our findings can explain the emergence of opaque goods sales as the outcome of some industries search for the optimal selling scheme.

ABSTRACT. The recommendation effect introduces a new rationale for product differentiation other than the usual motivation to reduce price competition. We introduce consumer learning in a version of Hotelling's model (1929) with sequential consumer purchases and a second dimension of variation, quality, about which the consumers have differential information. Due to consumer learning, firms are confronted with two offsetting effects: differentiation decreases the likelihood that a product is bought in earlier periods, but, by making inference more valuable, it also increases the likelihood that later consumers buy the differentiated good.

ABSTRACT. I study optimal contracting between a principal and an agent. Via an audit the principal can verify the agent's private information after the contract was executed, but cannot contractually commit to do so. Optimal contracting requires sophisticated communication. The privately informed agent reports her information to a mediator. The mediator draws a contract at random and recommends the principal whether to audit. Using a mediator allows for finetuning information transmission. All private information is revealed to the mediator, but the principal receives only as much information as is required to persuade her to audit. Simple communication, where the agent sends a message directly to the principal is typically not optimal. I characterize optimal mediated contracts, and provide comparative statics as regards to when audits are used, which distortions are imposed, and the minimal number of contracts. Additionally, I provide a lower bound on the principal's loss of using suboptimal communication.

ABSTRACT. We study how a principal should optimally choose between implementing a new policy and keeping status quo when the information relevant for the decision is privately held by agents. Agents are strategic in revealing their information, but the principal can verify an agent's information at a given cost. We exclude monetary transfers. When is it worthwhile for the principal to incur the cost and learn an agent's information? We characterize the mechanism that maximizes the expected utility of the principal. This mechanism can be implemented as a weighted majority voting rule, where agents are given additional weight if they provide evidence about their information. The evidence is verified whenever it is decisive for the principal's decision. Additionally, we find a general equivalence between Bayesian and ex-post incentive compatible mechanisms in this setting.

ABSTRACT. Economic decision-makers must commonly decide when to terminate temporary projects which are monitored imperfectly over time. I analyze the provision of dynamic incentives in an agent-assisted version of this problem. A firm must decide when to halt a project which yields a stochastic profit flow but eventually becomes unprofitable; the firm is aided by an agent with private information about the project's state, limited liability, and incentives for delayed project termination. I develop techniques for solving the resulting novel mechanism design problem, which features noisy verification of reports and limited transfers. The firm's optimal contract involves occasional inefficient early project termination but no late termination, a golden parachute which declines with proximity to termination, and soft deadlines exhibiting asymmetric sensitivity to news close to and far from termination.

ABSTRACT. In this paper, we analyze bankruptcy problems with nontransferable utility (NTU) from a game theoretical perspective by redefining corresponding NTU-bankruptcy games in a tailor-made way. It is shown that NTU-bankruptcy games are both coalitional merge convex and ordinal convex. Generalizing the notions of core cover and compromise stability for transferable utility (TU) games to NTU-games, we also show that each NTU-bankruptcy game is compromise stable. Thus, NTU-bankruptcy games are shown to retain the two characterizing properties of TU-bankruptcy games: convexity and compromise stability. As a first example of a game theoretical NTU-bankruptcy rule, we analyze the NTU-adjusted proportional rule and show that this rule corresponds to the compromise value of NTU-bankruptcy games.

ABSTRACT. This paper proposes a simple and general strategic approach for analyzing bankruptcy problems. We construct three strategic bargaining games and show that they yield unique subgame perfect equilibrium(SPE) outcomes that coincidewith the allocations given by the three prominent solution concepts, the constrained equal awards rule, the constrained equal losses rule and the Talmud rule, respectively. Moreover, we study the variations of these games for alternative solutions for bankruptcy problems as well as surplus sharing problems. We also discuss the robustness of the result in the presence of certain incomplete information. Center to all these bargaining protocols is an extended and context-fitting “divide-and-choose” mechanism.

ABSTRACT. We discuss the relationship between a TU game and a bankruptcy problem, and show how the bankrupt idea can give the solutions of cooperative games a new interpretation. In cooperative games, the players aim to get greater payoffs (or save more cost). Each player has an expected payoff after they get the worth of the grand coalition through cooperation. If the sum of their expectation exceeds the worth of the grand coalition, the game generates a bankruptcy problem. If the bankruptcy rules of the generated bankruptcy problem coincide with the solutions of the original game, we give the bankrupt interpretation for the solutions of the game. Our main contribution is thus to define the generated bankruptcy problem and explore the relations between the solutions of a TU game and the bankruptcy rules of the generated bankruptcy problem.

ABSTRACT. In the context of school choice, we experimentally study how behaviour and outcomes are affected when, instead of submitting rankings to the proposing or the receiving deferred acceptance mechanism (DA), participants make decisions dynamically, going through the steps of each DA. Our main results show that, (a) in the proposing DA, where it is a weakly dominant strategy to act according to the true preferences, participants switch slightly less while, (b) in the receiving DA, participants truncate more in the dynamic versions of the mechanisms than in the corresponding static versions. As a consequence, for most markets we test, no significant differences exist among the two versions of the proposing DA in what stability and average payoffs are concerned, but the dynamic version of the receiving DA delivers a clear improvement over its static counterpart on both dimensions.

ABSTRACT. It is well known that it is impossible for a strategyproof mechanism to Pareto dominate the celebrated Deferred Acceptance algorithm. However, it is unknown whether a mechanism can Pareto dominate DA in equilibrium when students play weakly undominated strategies. We demonstrate that a mechanism designer can do better by learning less about students’ preferences when making a school assignment. Specifically, we demonstrate that running DA but limiting students to only two applications always has an equilibrium in weakly undominated pure strategies that Pareto dominates DA. We also show that no mechanism that tries to Pareto improve DA directly has this property: no mechanism that Pareto improves DA with respect to submitted preferences actually Pareto improves DA in equilibrium. Finally, we introduce a new algorithm, Application with Automatic Appeals, and demonstrate that it also dominates DA in equilibrium. Unlike the 2-school DA, the Application with Automatic Appeals is nonwasteful.

ABSTRACT. This paper shows that three classic properties for bargaining solutions in an environment with a variable number of agents - Anonymity, Individual Monotonicity and Consistency - characterize a one-parameter class of Truncated Leximin solutions. Given a positive and possibly infinite $\alpha$, a Truncated Leximin solution gives each agent the minimum of $\alpha$ and their Leximin solution payoff.

ABSTRACT. Given a skew-symmetric matrix, the corresponding two-player symmetric zero-sum game is defined as follows: one player, the row player, picks a row and the other player, the column player, picks a column. The payoff of the column player is given by the corresponding matrix entry, the row player receives the negative of the column player. A randomized strategy is optimal for the column player if it guarantees an expected payoff of at least 0 independently of the strategy of the row player. We determine the probability that an optimal strategy for the column player randomizes over exactly k columns when the payoffs of the game are i.i.d. random variables that are symmetric around 0 and the game almost surely admits a unique optimal strategy. Our result has consequences for subclasses of symmetric zero-sum games and implies a result by Fisher and Reeves (1995) on tournament games.

ABSTRACT. In the early 1950s Lloyd Shapley proposed an ordinal and set-valued solution concept for zero-sum games called weak saddle. We show that all weak saddles of a given zero-sum game are interchangeable and equivalent. As a consequence, every such game possesses a unique set-based value.

ABSTRACT. An individual may display an honesty standard which allows her to lie a little with- out that being harmful to her self view as an honest person. An individual honesty standard is modeled as a subgroup of the society, including the individual herself. A partially-honest individual is an individual who strictly prefers to tell the truth prescribed by her honesty standard whenever lying has no exact on her material well-being. The paper studies the impact of placing honesty standard restrictions on the mechanism designer for Nash implementation problems of that society. It generates and shows that in an independent domain of preferences that condition is equivalent to Maskin-monotonicity, provided that honesty standards of society are non-connected. They are non-connected if every individual is excluded from the honesty standard of an- other individual.

ABSTRACT. In a partial equilibrium (PE) mechanism a sector authority (SA) aims to elicit agents' preference rankings for outcomes at hand, presuming separability of preferences, while such presumption is false in general. Therefore, its participants are required to behave as if they had separable preferences. This paper studies what can be Nash implemented if we take such misspecification of PE analysis as a given institutional constraint. The objective is to uncover the kinds of complementarity across sectors that this institutional constraint is able to accommodate. Thus, in our implementation model there are several SAs, agents are constrained to submit their rankings to each SA separately and, moreover, SAs cannot communicate with each other. When a social choice rule (SCR) can be Nash implemented by a product set of PE mechanisms, we say that it can be Nash implemented in PE. We identify necessary conditions and sufficient conditions

ABSTRACT. Dutta and Sen(2012) show that if there exists at least one partially honest agent, then no veto power is sufficient for partially honest implementation in Nash equilibria. Also, Kimya(2015) shows that if there are at least two partially honest agents, then unanimity is sufficient for partially honest implementation in Nash equilibria. While in Dutta and Sen(2012)'s mechanism and Kimya(2015)'s mechanism, each agent reports a preference prole, an outcome, and a positive integer, it is in fact unnecessary to ask agents to reveal a preference profile. We introduce an outcome mechanism in which each agent only reports an outcome and a positive integer from 1 to n. We show that the results of Dutta and Sen(2012) and Kimya(2015) are still valid by our mechanism with a smaller strategy space.

ABSTRACT. Generalized Nash Equilibrium (GNE) is an extension of the Nash equilibrium with extensive uses in real-world applications. Several numerical methods that compute this equilibrium exist, but very few computational ones capable do deal with large number of players. This paper explores the possibility of using an evolutionary algorithm for GNE approximation, based on differential evolution, and capable to compute several equilibria in a single run. Numerical experiments are used to illustrate the potential of this approach.

ABSTRACT. Bargaining is an important problem in economics literature. We simulate a population of agents adopting different strategies of the repeated Nash Demand Game and let it evolve. The result suggests that, when the game is a one-shot bargain, the 50-50 division is very stable. However, when the game is repeated (and/or the discount factor is sufficiently high), the 50-50 share is not that stable any more. Throughout the simulation, inefficient periods appear consistently. Upon closer inspection, these inefficient periods are due to aggressive strategies in the population. With this result, we would like to offer a way on a priori ground to explain why there is not always fairness in dividing a pie, and different societies may have different ways of sharing it.

ABSTRACT. Stochastic evolutionary games often share a dynamic property called punctuated equilibrium; this means that their sample paths exhibit long periods of stasis near one population state which are infrequently interrupted by switching events after which the sample paths stay close to a different population state, again for a long period of time. This has been described in the literature as a favorable property of stochastic evolutionary games. The methods used so far in stochastic evolutionary game theory, however, do not fully characterize these dynamics. We present an approach that aims at exposing the punctuated equilibrium dynamics by constructing Markov models on a reduced state space which approximate well this dynamic behavior. Besides having good approximation properties, the approach allows a simulation-based algorithm, which is appealing in the case of complex games.

ABSTRACT. Consider a Bertrand competition between firms which produce substitute goods on the one hand and many consumers with a common value on the other hand. Assume consumers receive some private signals regarding the identity of the superior product, inducing a demand uncertainty. Will such markets aggregate information? Will the superior firm necessary prevail? We study these questions in two scenarios - one in which consumers buy simultaneously and hence can not respond to each other's actions and another where buying is done sequentially. We provide necessary and sufficient conditions on the fundamentals of the problem- - the prior probabilities and signal distribution - to guarantee information aggregation and learning. We introduce a novel property over the signals, referred to as Vanishing Likelihood, which is necessary for social learning. Our results contribute to the literature of monopolistic entry deterrence on the one hand and herding on the other.

ABSTRACT. One of the central questions in game theory deals with predicting the behavior of an agent. Here, we study the inverse of this problem: given the agents’ equilibrium behavior, what are possible utilities that motivate this behavior? We consider this problem in arbitrary normal- form games in which the utilities can be represented by a small number of parameters, such as in graphical, congestion, and network design games. In all such settings, we show how to efficiently, i.e. in polynomial time, determine utilities consistent with a given correlated equilibrium. However, inferring both utilities and structural elements (e.g., the graph within a graphical game) is in general NP-hard. From a theoretical perspective our results show that rationalizing an equilibrium is computationally easier than computing it; from a practical perspective a practitioner can use our algorithms to validate behavioral models.

ABSTRACT. Whereas generating herds in the long run, rational observational learning can lead to behavior quite different from herding or imitation in the short run. This work revisits the canonical binary-state model of observational learning to investigate the possibility of non-imitative behavior generated by non-monotone learning: ceteris paribus, with some predecessor(s) switching to actions revealing greater confidence in one state of the world, agents become less confident in that state. We provide a necessary and sufficient condition for non-monotone learning, when agents are either uninformed or partially informed by binary private signals. In a general setting with continuous private signals, we provide a necessary condition for non-monotone learning and show that it fails only for information structures that never generate moderate public beliefs. We also provide two non-restrictive sufficient conditions for non-monotone learning under the general setting.

ABSTRACT. A model of tournament games is developed to characterize the set of tournaments where players never shirk in equilibrium. Outside of the set of such tournaments, the outcome can be a noisy indicator of players’ qualities, and factors such as cost of effort or heterogeneous prize spread may become irrelevant in players’ effort choices.

ABSTRACT. We study the optimal feedback policy in a dynamic tournament with strategic experimentation. In many situations performance feedback is needed for agents to evaluate the quality of their work and decide whether they need to try a new technique or work harder in order to secure a promotion. In a competitive setting the agent cares about winning the contest and his incentives are misaligned with a principal who cares about expected output. We show that the principal can re-align incentives by restricting the feedback she gives the agent to binary recommendations. In a setting where agents both choose technology and costly effort, binary recommendations continue to be the superior policy.

ABSTRACT. In this paper I analyze the attractiveness of rank-order tournaments if both market sides, employers and workers, can choose between payment systems. I consider workers’ self-selection into payment schemes, their effort provisions and the payment system choices of managers in a real-effort laboratory experiment. Depending on the stage of the experiment, workers are either randomly tied to a manager or choose a payment scheme (a fixed wage, a piece-rate or a rank-order tournament). Without worker choice a cheap (low-prize) tournament yields larger manager profits than a piece-rate. In environments with worker choice a clear self-selection pattern emerges: Productive workers select variable payment schemes (piece-rate and tournament), most workers prefer the piece-rate. Since the low-prize tournament is not chosen by productive workers it does not yield larger profits than the piece-rate anymore. These findings demonstrate that due to worker sorting rank-order tournaments are usually not simultaneously attractive for workers and employers.

ABSTRACT. We study communication via a neutral mediator between an informed sender and an uninformed decision maker with conflicting preferences in the framework of Crawford and Sobel (1982). We ask under what conditions introducing the mediator can provide higher ex-ante payoff to the decision maker than the most informative one-shot unmediated communication. Our model allows for players' preferences and distributions of the private information that generalize the commonly used uniform-quadratic specification. We identify intuitive sufficient conditions on the environment under which there exists a simple mediated equilibrium that strictly improves upon unmediated communication. As we show, the possibility of improving mediation depends crucially not only on the intensity of the conflict of interest between the players, but also on its sensitivity to the sender's private information.

ABSTRACT. This paper studies monotonic equilibria in a multi-sender version of Crawford and Sobel's (1982) cheap talk model, i.e. equilibria where senders' strategies are weakly monotonic in the state and where the receiver's strategy is strictly monotonic in the senders' messages. Monotonic equilibria have interval form, are bounded away from full revelation, and are straightforward to compute; they are closely related to the set of coordination-free equilibria identified by Lu (2015). When senders can be ranked according to bias: (i) in monotonic equilibria, senders most biased toward larger actions are informative when the receiver's desired action is smallest, and vice versa; and (ii) monotonic equilibria are collusion-proof in a strong sense. The monotonicity of sender strategies is shown to be a weak assumption if made alone, while the strict monotonicity of the receiver's strategy is motivated by the possibility of misunderstanding.

ABSTRACT. This paper explores the fault line that separates communication failure from success when message meaning is compromised because there is mutual but not common knowledge of which messages are available. If the size of the message space is just sufficient to convey all payoff-relevant private information, there may be communication failure at every finite knowledge order. In contrast, for any language state at which a "rich language" condition is satisfied -- the sender has second-order knowledge (belief) of having access to a large set of messages -- there exists an equilibrium that is language-interim optimal (optimal given available messages).

ABSTRACT. The paper is a contribution to the study of robustness in economic and social networks. Our robustness metric is based on network performance, which evaluates the system behavior and measures the flow or traffic among nodes. The paper develops a sequential model of network defense with two players, the Network Defender and the Network Attacker. The Network Defender chooses a node communication path that maximizes the information transmission inside the network by means of a Gravity model subject to node capacity constraints, and a set of network nodes to protect; protecting a node is costly. Then, the Network Attacker observes the defended network and decides whether to attack a set of network nodes. The subgame perfect equilibrium of this game is parameterized by the defense and attack costs. We also offer two instances of complex networks: Scale free networks and Poisson networks and numerically analyze the theoretical results.

ABSTRACT. Critical nodes control flows in a directed network and take advantage of these positions to extract excess rents. We extend this concept to critical node sets and investigate the potential contestation of these critical node sets by other node sets. This methodology allows us to introduce a game theoretic approach to analyse the formation of such critical node sets and of new network centrality measures that are based on potential membership of these critical node sets.

We introduce a non-cooperative game theoretic approach to network centrality based on the formation of certain critical node sets. We show that the Strong Nash equilibrium in a critical node set formation game identifies the maximally controlling critical node sets in any network. This provides a foundation to an algorithmic way to identify intermediation in directed networks. We develop applications to the Renaissance Florentine elite network and the networks formed by the 9/11 terrorists.

ABSTRACT. When players face uncertainty in choosing actions, undesirable outcomes cannot be avoided. Accidental defections caused by uncertainty, that does not depend on the level of care, require a mechanism to reconcile the players. This paper shows the existence of a perfect sorry equilibrium in a game of imperfect public monitoring. In the sorry equilibrium, costly apology is self-imposed in case of accidental defections, making private information public and allowing cooperation to resume. Cost of the apology required to sustain this equilibrium is calculated, the efficiency characteristics of the equilibrium evaluated and outcomes compared to those from other bilateral social governance mechanisms and formal legal systems. It is argued that with the possibility of accidental defections, other social mechanisms have limitations, while formal legal systems can generate perverse incentives. Therefore, apologies can serve as a useful economic governance institution.

ABSTRACT. This paper develops a game of asset ownership and environmental policy. Free-rider behavior in choosing pollution abatement is a major concern of international environmental policy design. Efficiency can be obtained, however, if each party receives less than the full share of its own profits from polluting. The remainder of the profits can be earned by other parties---in a reciprocal way. Swaps can be used to commit to share profits, hindering free-riding. The best climate policy thus may be swap contracts on asset markets.

ABSTRACT. Preventing situations leading to the prisoner’s dilemma game or to the stag hunt game can promote cooperation. So do providing incentives and establishing expectations, specifically hopes, as these promote cooperation in the repeated prisoner’s dilemma game: a small improvement in players’ expectations may improve the result of the game dramatically. Our analysis anchors game theory in social science, as an example for a general revision that we propose, in order to make game theoretical discussions part-and-parcel of the social sciences; this should make it more critical and its models empirically testable, thus rendering game theory more useful.

ABSTRACT. The paper develops a new behavioral model of trading and learning in markets called adaptive loss aversion. In the model, agents do not recognize that others have different information. Loss aversion makes them cautious about trading, which protects them from being exploited by better informed traders. The degree of loss aversion is adjusted in response to experience and carries over between games. A repeated market experiment with symmetric and asymmetric information is used to test the model. The model’s main predictions are supported, and it outperforms variants of quantal response equilibrium, analogy-based expectation equilibrium, cursed equilibrium and level-k.

ABSTRACT. By means of an experiment we identify subjects’ way of reasoning without an econometric model and restricting assumptions. We elicit subjects’ probabilistic beliefs about their opponent in a series of one-shot bimatrix games without feedback. Using Selten’s Measure of Predictive Success (MPS) and a parametric bootstrap we investigate if subjects follow the reasoning concepts level-k (Lk), quantal response equilibrium (QRE), or utility proportional beliefs (UPB). We find that for about 80 percent of subjects the concept with the highest MPS also performs better than random in explaining subjects’ beliefs. On the other hand, only 45 percent of our subjects state beliefs as if they reason according to a fixed concept across all games. Finally, we confirm the hypothesis that subjects make choices based on their beliefs, although it is not a deterministic relationship. Subjects best-respond to their stated beliefs with a high probability if incentives are high.

ABSTRACT. In the current literature, there is a lively debate about whether a level-k model can be based on salience to explain behaviour in games with distinctive action labels such as hide-and-seek or discoordination games. This study presents seven different experiments designed to measure salience. When based on any of these empirical salience measures, the standard level-k model does not explain hide-and-seek behaviour. Modifying the model such that players follow salience when payoffs are equal, the model fits hide-and-seek data well. However, neither the original nor the modified model account for data from a discoordination game. This holds true even when basing the level-k prediction on participants' own individual salience assessments.

ABSTRACT. In this paper, several characterizations of the Owen and Banzhaf-Owen values are provided. All the characterizations make use of a property based on the principle of balanced contributions. This property is called the intracoalitional balanced contributions property and was defined by Calvo et al.

ABSTRACT. We present an axiomatic characterization of the Owen-Shapley spatial power index for the case where issues are elements of two-dimensional space. This characterization employs a version of the transfer condition, which enables us to unravel a spatial game into spatial games connected to unanimity games. The other axioms include two conditions concerned particularly with the spatial positions of the players, besides spatial ver- sions of anonymity and dummy. The last condition says that dummy players can be left out with changing the power of the other players; we show that this condition can be weakened by requiring dummies to have zero power, at least if we add a condition of continuity. We also show that the axioms in our characterization(s) are logically independent.

ABSTRACT. It is shown that simple and coalitional strategy-proofness of a voting rule on the full weakly unimodal domain of a convex idempotent interval space are equivalent properties if that space satisfies interval anti-exchange, a basic property also shared by a large class of convex geometries including trees and Euclidean convex spaces. It is also established that a much weaker minimal anti-exchange property is necessary to ensure equivalence of simple and coalitional strategy-proofness in that setting. An immediate corollary to that result is that such `unimodal' equivalence fails to hold both in certan median interval spaces including those induced by bounded distributive lattices that are not chains, and in certain non-median interval spaces including those induced by partial cubes that are not trees.Thus, it turns out that anti-exchange properties of the relevant interval space provide a powerful general common principle to explain the varying relationship between simple and coalitional strategy-proofness interval.

ABSTRACT. Communication is fundamental to elections. This paper extends canonical voter turnout models to include any form of communication, and characterizes the resulting set of correlated equilibria. In contrast to previous research, high-turnout equilibria exist in large electorates and uncertain environments. This difference arises because communication can be used to coordinate behavior in such a way that voters find it incentive compatible to always follow their signals past the communication stage. The equilibria have expected turnout of at least twice the size of the minority for a wide range of positive voting costs, and show intuitive comparative statics on turnout: it varies with the relative sizes of different groups, and decreases with the cost of voting. This research provides a general micro foundation for group-based theories of voter mobilization, or voting driven by communication on a network.

ABSTRACT. Representatives from differently sized constituencies form an assembly which takes political decisions by a weighted voting rule and adopts the ideal point of the weighted median amongst them. Preferences of each representative are supposed to coincide with the constituency's median voter. Analytic results by Kurz et al. (2014) for infinite chains of assemblies suggest that individual voters' a~priori influence on the collective decision can be equalized by allocating voting weight proportional to the square root of constituency sizes. The paper investigates performance of this simple square root rule and sophisticated variations that are based on the Shapley value or the Penrose-Banzhaf power measure. Monte Carlo simulations indicate that power index-based rules are superior to simple rules when the number of constituencies is "small".

ABSTRACT. We consider two properties for the assignment problem. The first one is inspired by the Minimal Rights First property for the bankruptcy problem: assigning to agents their minimal core allocation, adjusting the value created accordingly and sharing the value created gives the same shares as if we share the value created in the original problem. The second property considers problems in which agents have no better option than to partner up with their optimal match. Since agents have no reasons to threaten to secede with another partner, the values for other matches should not impact the shares. We show that these properties, together with stability, yield the extreme points of the core of Demange (1982) and Leonard (1983), as well as their weighted averages. Adding Symmetry, we characterize the Fair Division solution of Thompson (1981). We also provide a new method to compute the minimal core allocations.

ABSTRACT. Often, sets of objects must be divided without cash changing hands: inheritance among siblings, shifts among interchangeable workers, seats in overbooked classes, computing resources in peer-to-peer platforms, etc. We assume additive utilities, and that we can divide a limited number of objects, by time-sharing or randomization. The two prominent solutions are the Relative Equivalent (REG) solution, and the Nash MaxProduct, NMP (aka the Competitive Equilibrium with Equal Incomes, CEEI). With three or more participants, NMP outperforms REG: unlike the latter, NMP meets the No Envy property and all agents benefit from the addition of new objects; and NMP is often “integral” (does not divide any object). Moreover NMP rule induces truthful reports if preferences about objects an agent receives are verifiable ex post, so that misreporting affects only the objects lost to this agent. Together with Efficiency, Symmetry and Scale Invariance, this Verification-proofness property in group form characterizes NMP rule.

ABSTRACT. We study the monotonicity properties of solutions in the classic problem of fair cake-cutting - dividing a heterogeneous resource among agents with different preferences. Resource- and population-monotonicity relate to scenarios where the cake, or the number of participants in the division, changes. They require that the utility of all participants change in the same direction: either all of them are better-off (if there is more to share) or all are worse-off (if there is less). We show that classic fair cake-cutting protocols fail to be monotonic. We then present monotonic division rules in two utility models. When utilities are additive, several proportional and Pareto-optimal division rules satisfy one or both monotonicity axioms. In contrast, when utilities have a connectivity constraint, no proportional and Pareto-optimal rule can satisfy any monotonicity axiom. Relaxing the requirement to weak-Pareto-optimality, we show a resource-monotonic protocol for two agents and some population-monotonic rules for n agents.

ABSTRACT. ‘Noise’ in this study, in the sense of evolutionary game theory, refers to deviations from prevailing behavioral rules. Analyzing data from a laboratory experiment on coordination in networks, we tested ‘what kind of noise’ is supported by behavioral evidence. This empirical analysis complements a growing theoretical literature on ‘how noise matters’ for equilibrium selection. We find that the vast majority of decisions (96%) constitute myopic best responses, but deviations continue to occur with probabilities that are sensitive to their costs, that is, less frequent when implying larger payoff losses relative to the myopic best response. In addition, deviation rates vary with patterns of realized payoffs that are related to trial-and-error behavior. While there is little evidence that deviations are clustered in time or space, there is evidence of individual heterogeneity.

ABSTRACT. In many markets, new technologies allow traditional jobs to be divided into discrete tasks that are widely distributed across workers and dynamically priced given prevailing supply and demand conditions. This "sharing" or "gig" economy represents a more flexible work system, and is most common in two-sided markets in which a firm acts as a platform to connect service providers and consumers. One prominent example of this is the ride-sharing company Uber, which connects riders and driver-partners, and dynamically prices trips using a system known as surge pricing. In this talk, I discuss the practical problems of designing such a dynamic pricing system, how that dynamic pricing coordinates workers who can now earn compensation on a flexible schedule, and more broadly how the "gig" economy is evolving and growing as a form of market organization.

ABSTRACT. The price of anarchy is a measure of the inefficiency of selfish behavior that has been successfully analyzed in many applications, including network routing, resource allocation, auctions, and even models of basketball. It is defined as the worst-case ratio between the welfare of a Nash equilibrium and that of an optimal (first-best) solution. Seemingly, a bound on the price of anarchy is meaningful only if players successfully reach some Nash equilibrium. The main result of this paper is that for many of the classes of games in which the price of anarchy has been studied, results are "intrinsically robust": a bound on the worst-case price of anarchy for pure Nash equilibria *necessarily* implies the exact same worst-case bound for much larger sets of outcomes, including mixed Nash equilibria, correlated equilibria, and sequences of outcomes generated by natural experimentation strategies (such as successive best responses or simultaneous regret-minimization). We also discuss subsequent developments, such as generalizations to incomplete-information games with applications to mechanism design.

ABSTRACT. Many studies across species have explored the nature and neural basis of strategic thinking (often called "mentalizing" in psychology and other sciences). This talk summarizes what is known, with an emphasis on cognitive hierarchy models in which agents can think strategically at more or fewer levels of depth.

ABSTRACT. We consider a simple model of neural decision making in which there is a limited capacity to make fine distinctions. This implies that the evolutionarily optimal hedonic utility function must adapt to the circumstances. The new result here is that there are readily implementable mechanisms by which utility functions adapt rapidly, in real time. That is, if the distribution of rewards shifts, the utility function reacts, to maintain optimal use of the limited capacity to discriminate. Such rapid adaptation of utility is analogous to well-known properties of the visual system, and might well be implemented by similar neural circuitry. In the case that all that matters is the probability of error, the mechanism is particularly simple. If the criterion is instead to maximize expected fitness, we find a mechanism that is approximately optimal.

Although such adaptive utility functions take an hedonic interpretation of preference seriously, and incorporate large swings in levels, they are at once approximately consistent with conventional economics. That is, the possibility of suboptimal choice stems only from the limited capacity to make fine distinctions. As this capacity improves, utility remains adaptive, but choice becomes fully optimal.

ABSTRACT. Owing to the worldwide shortage of deceased donor organs for transplantation, living donations became a significant source of transplant organs. However, not all willing donors can donate to their intended recepients because of medical incompatibilities. These incompatibilities can be overcome by an exchange of donors between patients. Such exchanges have become widespread in the last decade for kidneys with the introduction of optimization and market design techniques to kidney exchange. A small but growing number of liver exchanges has also been conducted. Over the last two decades a number of transplantation procedures emerged where organs from multiple living donors are transplanted to a single patient. Prominent examples include dual-graft liver transplantation, lobar lung transplantation, and simultaneous liver-kidney transplantation. Exchange, however, is neither practiced nor introduced in this context. We introduce multi-donor organ exchange as a novel transplantation modality, provide a model for its analysis, and introduce optimal exchange mechanisms under various logistical constraints. Our simulations suggest that living-donor transplants can be significantly increased through multi-donor organ exchanges.

Joint work with Haluk Ergin and Tayfun Sonmez.

ABSTRACT. We analyze a dynamic model of judicial decision making. A court regulates a set of activities by allowing or banning them. In each period a new case arises and the appointed judge has to decide whether the case should be allowed or banned. The judge is uncertain about the correct ruling until she conducts a costly investigation. We compare two institutions: persuasive precedent and binding precedent. Under persuasive precedent, the judge is not required to follow previous rulings but can use the information acquired in an investigation made in a previous period. Under binding precedent, however, the judge must follow previous rulings when they apply. We analyze both a three-period model and an infinite-horizon model. In both models, we find that the incentive to acquire information for the judge is stronger in earlier periods when there are few precedents under binding precedent than under persuasive precedent, but as more precedents are established over time, the incentive to acquire information becomes weaker under binding precedent than under persuasive precedent.

Joint work with Ying Chen at Johns Hopkins University.

ABSTRACT. The overarching goal of the presentation is to analyze the (arguably) main game-theoretic (or rather: inspired by game theory) insight into the nature of law, namely that the law (legal rules) can be plausibly regarded as a convention. The presentation is divided into four parts. The first part provides an overview of the various accounts of the concept of convention which were proposed both within game theory and philosophy. It also highlights the complex relations between these accounts. The second part is devoted to the problem of which of these accounts best illuminate the nature of law (legal rules) and what assumptions regarding the law they presuppose. The third part deals with the limits to understanding law (legal rules) as a convention.

In the last part a certain paradox regarding the conventional nature of law is formulated. The paradox can be roughly stated as follows. Conceiving law as convention seems to imply what may be called a 'strategic' conception of legal validity, according to which legal norms are valid only if they are generally, or almost generally, followed and/or regarded as valid in a society (which implies that an agent does not have a prima facie duty to obey a legal norm if the other agents with whom she interacts or may interact do not follow and/or do not regard as valid this norm). The paradox arises from the fact that conceiving law as a convention is typical for the adherents of legal positivism which, arguably, implies a non-strategic account of validity, according to which a norm is valid if it has been enacted in accordance with a proper procedure (and thereby it is irrelevant for its validity whether it is generally, or almost generally, followed and/or regarded as valid).

ABSTRACT. Equilibrium bidding strategies in combinatorial auctions are not well understood. Ex-post split-award auctions are a wide-spread form of combinatorial procurement auctions, in which the demand for some quantity to be procured is split into two or more shares. We focus on markets with n > 2 bidders and diseconomies of scale, which is practically relevant and strategically challenging, since bidders have to coordinate on the efficient outcome. We show that the first-price sealed-bid and the Dutch ex-post split-award auction are not strategically equivalent. The sealed-bid format exhibits a coordination problem for bidders, whereas the Dutch has a unique and efficient equilibrium. Hence, it is possible to characterize conditions, for which a buyer should strictly prefer the Dutch over the first-price sealed-bid auction. We also provide a welfare analysis and compare purchasing costs of both first-price auctions to the Vickrey-Clarke-Groves and descending auction.

ABSTRACT. We characterize the complete set of pure-strategy Nash equilibria of a class of sealed-bid combinatorial auctions. The class contains any auction that assigns bundles to maximize the sum of bids and chooses payments between the reported social opportunity cost for the bundle won and the bid amount. We rank equilibria of prevalent auctions in this class, finding that the equilibria of the pay-as-bid (PAB) auction are a subset of the equilibria of bidder-optimal core-selecting (BOCS) auctions, which are in turn a subset of the equilibria of the Vickrey auction. Characterizing the equilibrium outcomes, we find that any assignment and payments that generate individually rational payoffs can result from some equilibrium of the Vickrey and BOCS auctions, whereas possible outcomes of the PAB auction are more limited. We consider extensions of the auction games to address the seller's incentives, the impact of budget constraints, and the implementation of the tie-breaking rule.

ABSTRACT. We investigate if and how revenue-maximizing auctioneers restrict combinatorial bidding in the presence of auctioneer competition. Two sellers offer the same set of two heterogeneous items to six bidders. Each bidder desires either one of the two items or the package of the two items. First, each seller decides on which packages to allow bidders to submit bids in a VCG mechanism. Then, each bidder selects which one of the two sellers' auctions to participate in. We find that sellers will not both offer an unrestricted VCG mechanism, i.e., a combinatorial auction. Rather they will segment the market via their respective choice of allowable package bids: One seller will attract bidders who desire a single item; the other seller will attract bidders who desire both items.

ABSTRACT. We consider a new, dynamic price search model with fixed or random deadlines to study in detail how consumers search within and across stores during a single search spell. To endogenize the intensity of competition, we allow firms to adjust freely the level of frictions in their online stores. Interestingly, this pins down uniquely the numbers of informed and uninformed consumers. We show that there exist two inefficient equilibria, both with a prominent firm and a non-prominent firm, where these numbers are exactly the same. The outcome is thereby precisely halfway between Diamond equilibrium and Bertrand equilibrium.

ABSTRACT. We combine agency theory with product market competition to study the strategic properties of rivals' contract decisions for cost-reducing innovations and the relationship between risk and incentives. We show that a change in risk may trigger asymmetric responses of rivals in the same market: lower risk may induce some firms to strengthen, while other firms to weaken the incentives provided to their agents. This result holds regardless of the mode of competition in the product market, Cournot or Bertrand, as long as the rivals' R&D decisions are strategic substitutes. Our model generates new empirical implications and can provide an explanation for the lack of strong empirical support in the literature for a negative relationship between risk and incentives. It also has policy implications about the effect of risk on the incentives to innovate.

ABSTRACT. This paper shows that a firm may benefit from restricting its capacity, in order to trigger herding behaviour from consumers in situations where such behavior is overwise unlikely. We consider a setting with social learning, where consumers observe sales from previous cohorts and update beliefs about product quality before making their purchase decision. Imposing a capacity constraint effectively results in coarser available information: following a sell-out, consumers cannot infer the exact level of demand, but instead attach positive probability to all levels of demand that exceed capacity. The resulting discrete jump in beliefs about quality following a sell-out benefits the firm. However, the capacity constraint also hurts the firm by directly limiting potential sales. We show that, under certain condition, the informational concern prevails and it is optimal for a firm restrict its capacity.

ABSTRACT. Price-setting multi-product suppliers have access to multiple sources of information about demand conditions, where the publicity of each source corresponds to the cross-industry correlation of signals received from it. A signal's influence on suppliers' prices is increasing in its publicity as well as in its precision. The emphasis on relatively public information is stronger for smaller suppliers who control narrower product portfolios. When information is endogenously acquired, suppliers listen to only a subset of information sources. This subset is smaller when products are less differentiated and when the industry is less concentrated. Smaller suppliers focus attention on fewer information sources. The inefficiencies arising from information acquisition and use are identified. The associated externalities depend upon the extent of product differentiation, the concentration of the industry, and the degree of decreasing returns to scale.

ABSTRACT. We analyse a dynamic model of investment under uncertainty in a duopoly where firms have an option to switch from one market to another. We construct a subgame perfect equilibrium in Markovian mixed strategies and show that both preemption and attrition can occur along typical equilibrium paths. This changes the nature of stopping problems to be solved, compared to existing strategic real option models. Equilibrium outcomes differ qualitatively from those of the model’s deterministic version. Competition endogenously determines the firms’ exposure to the two markets’ risk factors, one of which is indeed eliminated by the mixed strategies in equilibrium.

ABSTRACT. This talk has been cancelled.

ABSTRACT. Reputation models typically assume players have full memory, yet in many applications this does not hold. This paper studies incomplete information games where players observe only finitely many recent periods, deriving a recursive characterization of the equilibrium payoff set that captures both stationary and previously unexplored non-stationary equilibria, as well as tools for studying purifiable (i.e. robust to payoff perturbations) equilibria. These tools are applied to a product choice game. For 1-period memory, I obtain the exact minimum and maximum purifiable equilibrium payoffs for almost all discount factors and prior beliefs on an "honest" firm type. For long memory, I characterize the minimum purifiable (non-stationary) equilibrium payoff and unique stationary payoff. In both cases, incomplete information and non-stationary behavior qualitatively change the equilibrium payoff set. These results hold for fixed discount factors independent of prior beliefs, and so do not require extreme patience.

ABSTRACT. We study a canonical model of reputation between a long-run player and a sequence of short-run opponents, in which the long-run player is privately informed about uncertain state, which determines the monitoring structure in the reputation game. The long-run player plays a stage-game repeatedly against a sequence of short run opponents. We present necessary and sufficient conditions (on the monitoring structure and type space) to obtain reputation building in this setting. Specifically, in contrast to the previous literature, with only stationary commitment types, reputation building is generally not possible and highly sensitive to the inclusion of other commitment types. However with the inclusion of appropriate dynamic commitment types, reputation building can again be sustained while maintaining robustness to the inclusion of other arbitrary types.

ABSTRACT. Players (people, firms, states, etc.) have privacy concerns that may affect their choice of actions in strategic settings. We use a variant of signaling games to model this effect and study its relation to pooling behavior, misrepresentation of information, and inefficiency.

ABSTRACT. Preserving privacy is a concern in auctions and exchanges. To examine the role of privacy in markets, this paper suggests an alternative to differential privacy (Dwork (2006)) that accommodates settings in which outcomes of a mechanism respond to incentives. We formulate a class of mechanism design problems based on the uniform-price market clearing to study the joint design of bid schedules (contingent variables); transparency of auction outcomes (observables); and the timing of market clearing. A design preserves privacy if the publicly observable outcome is not informative about the participants' private information. We show that this privacy requirement can be necessary for the viability of the market -- if violated, equilibrium may not exist. However, there need not be a trade-off between privacy preservation and welfare. In particular, we derive constructive solutions to show that privacy-preserving designs can be efficient.

ABSTRACT. We study self-selection in centralized school choice, a strategic behavior that takes place when students submit preferences before knowing their priorities at schools. A student self-selects if she decides not to apply to some schools despite being desirable. We give a theoretical explanation for this behavior: if a student believes her chances of being assigned to some schools are zero, she may not rank them even when the mechanism is strategy-proof. Using data from Mexico City high school match, we find evidence that self-selection exists, and has negative consequences for low income students as a result of their strategic mistakes.

ABSTRACT. School districts have been considering to allow violations of priorities at certain schools to improve students' welfare. Inspired by this, we generalize the school choice problem by allowing such violations. We characterize set of constrained efficient outcomes for school choice problem in this setting. We introduce a class of algorithms, Student Exchange under Partial Fairness (SEPF), which guarantees to find constrained efficient matching. Moreover, any constrained efficient matching Pareto dominating the Student Optimal Stable Matching can be obtained via a member of thisclass. A similar approach to improve students' welfare is to ask students' consent for violation of their priorities (Kesten(2010)). The idea is that each student weakly benefits from this weakening of stability. Clearly, this welfare gain depends on students' having incentives to consent. We identify the unique rule, Top Priority Rule, within thisclass, giving each student incentives to consent. Uniqueness result implies it is equivalent to Kesten's EADAM.

ABSTRACT. epsilon-equilibrium allows for worse actions to be played with higher probability than better actions. I introduce a refinement that addresses this shortcoming: an epsilon-equilibrium is monotonic if each player assigns (weakly) higher probabilities to better actions. This concept is logically independent of strong epsilon-equilibrium. I study these refinements of epsilon-equilibrium in games with countably many players and finitely many pure strategies, and prove the existence of monotonic epsilon-equilibrium in a special class of such games---strongly symmetric games. The proof is constructive and it implies, in particular, the existence of symmetric epsilon-equilibrium in strongly symmetric games. This result fails to hold in the larger class of weakly symmetric games.

ABSTRACT. Multi-player perfect information games are known to admit a subgame-perfect epsilon-equilibrium, for every epsilon>0, under the condition that every player’s payoff function is bounded and continuous on the whole set of plays. In this paper, we address the question on which subsets of plays the condition of payoff continuity can be dropped without losing existence. Our main result is that if payoff continuity only fails on a sigma-discrete set (a countable union of discrete sets) of plays, then a subgame-perfect epsilon-equilibrium, for every epsilon>0, still exists. For a partial converse, given any subset of plays that is not sigma-discrete, we construct a game in which the payoff functions are continuous outside this set but the game admits no subgame-perfect epsilon–equilibrium for small epsilon > 0.

ABSTRACT. We examine a type of zero-sum games that highlights the differences between modeling strategies as countably-additive measures and modeling them as finitely-additive measures. The solutions of these games are essentially different for these two classes of strategies, and when using countably-additive strategies, the solutions depend heavily on set theoretic axioms.

ABSTRACT. We move towards a more robust theory of individual behavior in mechanism design by allowing hierarchies of players with varying but bounded ``depths of rationality''. Specifically, we study (full) implementation with complete information when players are at least rational and at most k-rational. In ``independent domain of preferences'' (IDP) environments, we obtain a revelation principle: A social choice function (SCF) is implementable if and only if it is implementable by its associated direct mechanism. Two conditions characterize such SCFs: Strategy-proofness and ``strong non-bossiness''. For non-IDP environments, we provide simple necessary and sufficient conditions as well as characterization of implementable SCFs. We also present results for the case when rationality is at least mutual knowledge. There is a significant gap between implementation when rationality is at least mutual knowledge compared to when it is not. However, it does not make a significant difference whether rationality is mutual knowledge or common knowledge.

ABSTRACT. Canonical mechanisms have unattractive features because they have to cover every instances of the implementation problem. This is unavoidable but at the same time it leaves open whether these features can be avoided in all specific cases or even most of them. We focus on one such feature: The infinity of the message space. It has been know since Jackson [A crash course in implementation theory, Soc Choice Welfare 18 (2001) 655-708.] that allowing only finite message spaces is a constraint. What is not known, however, is how bad this constraint is. Not surprisingly it all depends on what is known about the utility representations. What is surprising, though, is that allowing only finite message spaces does not severely limit implementability. In economic environments the constraints are particularly weak.

ABSTRACT. This talk has been cancelled.

ABSTRACT. We show that under the logit dynamics, positive feedback among agents (also called bandwagon property) induces evolutionary paths along which agents tend to repeat the same actions consecutively so as to take full advantage of the feedback effects. In particular, for paths escaping the domain of attraction of a given equilibrium---called a convention---positive feedback implies that along the minimum cost escaping paths, agents always switch away from the status quo convention strategy. In addition, the relative strengths of positive feedback effects impose a particular ordering on alternative strategies to which transitions occur in the minimum cost path. Using these two effects, we demonstrate that the optimal paths involve only the same repeated mistakes by agents. From our results on the exit problem, we then characterize stochastically stable states under the logit choice rule for a class of non-potential games with an arbitrary number of strategies.

ABSTRACT. We study environments in which agents are randomly matched to play the Prisoner's Dilemma, and each player observes a few of the partner's past actions against other opponents. We depart from the existing literature in two key aspects: (1) we allow few agents in the population to be commitment types, and (2) we do not assume a time zero in which the entire community start interacting. We show that the presence of few committed agents destabilizes the existing mechanisms to sustain cooperation, and we present a novel mechanism (which is essentially unique) that sustains stable cooperation in many environments.

ABSTRACT. In voluntarily separable repeated Prisoner's Dilemma, many neutrally stable distributions as defined in Fujiwara-Greve and Okuno-Fujiwara (2009) are vulnerable to "secret-handshake" mutants. In particular, the fundamentally asymmetric equilibrium of cooperators and myopic defectors, which was shown to be often more efficient than any trust-building equilibrium, is not neutrally stable. However, evolutionary stability is restored when mutation is sufficiently diverse to include exploiters of secret-handshake mutants. In a large society, diverse mutation occurs naturally. The boundary distributions of the sufficiently diverse mutant distributions correspond to payoff-equivalent equilibria to the original equilibrium, because they internalize the incumbent strategy distribution at points when partnerships end. Therefore, diverse actions at many turning points of long-term partnerships are not a non-convergence event but an equilibrium phenomenon.

ABSTRACT. We report two information cascade game experiments that directly test the impact of altruism on observational learning. Participants play the cascade game in two parallel sequences, the observed and the unobserved sequence. Only the actions of the observed entail informational benefits to subsequent participants. We find that observed contradict their private information significantly less often than unobserved when the monetary incentives to follow others are moderately weak. Unobserved are slightly reluctant to contradict their private information only when the monetary incentives to follow others are the weakest. Once the monetary incentives to follow others are strong enough observed contradict their private information to the same extent as unobserved. Long laboratory cascades accumulate substantial public information which in turn often increases the earnings of participants. In Experiment 2, participants are offered better opportunities to learn about the strategies played by observed which amplifies the impact of altruism on observational learning.

ABSTRACT. This paper investigates the emergence of cooperation in a heterogeneous population. The population is divided into two cultural groups. Agents in the population are randomly matched in pairs to engage in a prisoner dilemma. The matching process is assortative, that is, cooperators are more likely to be matched with cooperators, defectors are more likely to be matched with defectors. When two agents of different cultures are matched, they suffer a cost due to their cultural differences. We call such a cost cultural aversion. We find that when cultural aversion is sufficiently strong, perfect correlation between culture and behavior emerges: all agents from one cultural group cooperate, while all agents from the other cultural group defect.

ABSTRACT. We study round-robin tournaments with either three or four symmetric players whose values of winning are common knowledge. In the round-robin tournament with three players we characterize the sub-game perfect equilibrium and show that each player maximizes his expected payoff and his probability to win if he competes in the first and the last stages of the tournament. In the round-robin tournament with four players we characterize the sub-game perfect equilibrium and show that a player who plays in the first match of each of the first two rounds has a first-mover advantage as reflected by a significantly higher winning probability as well as a significantly higher expected payoff than his opponents.

ABSTRACT. In this study we investigate the extension of Hoteling-Downs model to the case where the preferences of the voters do not have to be single-peaked. Where the classical results show that the equilibrium point is unique, we show that the result is robust under small perturbations. However, the structure of the model and the equilibrium change when the perturbations are not small. We provide examples and define a criteria which describe the structure of the equilibrium points when the tie situation has been resolved by perturbation.

ABSTRACT. This paper introduces private sender information in a game of Bayesian persuasion with monotonic sender preferences. I derive properties of increasing differences related to the precision of signals and use these to characterize the set of equilibria selected by the D1 criterion. These equilibria are either separating, i.e., the sender's choice of signal reveals his private information to the receiver, or fully disclosing, i.e., the outcome of the sender's chosen signal fully reveals the payoff-relevant state. If full disclosure is optimal for all sender types, then the equilibrium is fully disclosing. Otherwise, the equilibrium is fully separating and incentive compatibility requires the sender to use signals that are strictly more informative than the ones that would be used under symmetric information. Therefore, when full disclosure is suboptimal the sender incurs a cost in comparison to the symmetric information case, while the receiver obtains better information and extracts an "ignorance rent."

ABSTRACT. We develop a multi-receiver framework of Bayesian persuasion to show that banking supervisors’ disclosure of macroprudential stress tests can be designed in a way that increases welfare. We show that through an optimal disclosure mechanism macroprudential authorities are able to provide valuable information to actors in the financial system, thereby increasing their decision- making quality and ensuring the well-functioning of financial markets. Even if the optimal mechanism exposes macroprudential authorities to uncertainty which would not exist without informative disclosure of macro stress tests, we show that authorities are able to exploit uncertainty in a way beneficial to financial market actors. In the light of Basel III, our theory may help explaining the rising importance of macro stress tests and how they should be designed.

ABSTRACT. This paper studies a variation of the Bayesian persuasion model in which the sender's commitment to a signaling device binds with probability less than one. The receiver knows the commitment probability but cannot tell whether the commitment is binding or not. We first show that the sender is weakly better off as the commitment probability increases. Then, we study the model in a specific environment: the uniform-quadratic case. In the uniform-quadratic case, we show that for any level of the sender's bias (even when the bias is arbitrarily high), both players are strictly better off as they move from the no-commitment through the partial-commitment to the full-commitment case. To establish the strict welfare improvement from the no-commitment to the partial-commitment case, it suffices to consider only three types of signaling devices. Interestingly, one of them can achieve the best outcome in Blume et al. (2007) and Goltman et al. (2009).

ABSTRACT. In this paper, we generalize the General Lotto game (budget constraints satisfied in expectation) and the Colonel Blotto game (budget constraints hold with probability one) to allow for battlefield valuations that are heterogeneous across battlefields and asymmetric across players, and for the players to have asymmetric resource constraints. We completely characterize Nash equilibrium in the generalized version of the General Lotto game and find that there exist sets of non-pathological parameter configurations of positive Lebesgue measure with multiple payoff nonequivalent equilibria. Across equilibria each player achieves a higher payoff when he more aggressively attacks battlefields in which he has lower relative valuations. Hence, the best defense is a good offense. We then show how this characterization can be applied to identify equilibria in the Colonel Blotto version of the game.

ABSTRACT. The classical Colonel Blotto game is the earliest game to model conflicts in multiple battlefields. In this paper, we extend the Colonel Blotto game to a sequential attacker-defender game where defender can redeploy its resources after observing the attacker's deployment. Our goal is to understand the value of this redeployment option in such games, and understand its impact on both player's strategy. In general, finding an equilibrium strategy in this game is challenging. We obtained an equivalent reformulation of the game using a conic program. By analyzing this equivalent reformulation, we can obtain many interesting properties of the game. We further explore how the redeployment network structure affects the game, showing that a sparse redeployment network structure can already capture the value of redeployment for the defender, and thus he does not need to establish full or dense flexible redeployment network structure to achieve high level of performance.

ABSTRACT. We analyze the problem of a single player who is threatened by a coordinated attack. For example, consider a central bank defending a currency peg, a government facing a revolution or a prison warden trying to prevent a riot. The defending player would like to deter his opponents from attacking by using their coordination problem against them and thus exerting as little resources as possible. Bentham (1787) proposed the “panopticon”, an innovative prison concept, as an ideal solution to this problem. We consider different information structures in a stylized model of a prison. We show that Bentham’s intuition was correct and that the panopticon often performs best, especially if there are many prisoners. This provides recommendations for the more general problem of defense against coordinated attacks as well as insights into the applications of Bentham’s ideas across the social sciences.

ABSTRACT. Weak property rights encourage rival value appropriation vis-a-vis own value creation. But value destruction due to appropriative conflicts can encourage collective action towards improving property rights. We consider two countries (communities), initially situated in anarchy, differentially-endowed in initial resources, and populated by a sequence of generations. In every generation, the countries' myopic citizens agree on 'nudges' to the inherited property rights regime by mutual consent, and then decide on value creation vs. appropriation. When initial resource inequality is low and /or past consumption is the major force behind resource growth, perfect property rights can emerge in the long-run. But high initial resource inequality and/or the dominance of past productive investments in determining future resource growth perpetuates anarchy.

ABSTRACT. Different procedures are used to implement the challenge of prospective jurors by the parties to a trial. Judges and legislators typically care for procedures which limit the parties’ ability to strategize against one another. This paper compares some of the most commonly used procedures in terms of the room they leave for strategizing. No procedure in a wide class that includes all procedures used in practice is completely immune to strategizing. The rationality threshold of a procedure (i.e. the number of rounds of iterated elimination of strategies which are never best responses needed to reach an equilibrium) can however be used to measure procedures’ degree of strategic involvement. Based on this measure, so-called struck procedures leave less room for strategizing than so-called strike and replace procedures. Sequential procedures also tend to have a lower rationality threshold than simultaneous ones.

ABSTRACT. We study a legislative bargaining game in which failure to agree in a given round may result in a breakdown of negotiations. In that case, each player receives an exogenous `disagreement value'. We characterize the set of stationary subgame perfect equilibria under all q-majority rules. Under unanimity rule, equilibrium payoffs are strictly increasing in disagreement values. Under all less-than-unanimity rules, expected payoffs are either decreasing or first increasing and then decreasing in disagreement values. We conduct experiments involving three players using majority and unanimity rule, finding support for these predictions.

ABSTRACT. Predictions under common knowledge of payoffs may differ from those under arbitrarily, but finitely, many orders of mutual knowledge; Rubinstein's email game is a seminal example. Weinstein and Yildiz (2007) showed that the discontinuity in the example generalizes: for types with multiple rationalizable actions, there exist similar types with unique rationalizable action. Call this the "WY-discontinuity." We study the robustness of the WY-discontinuity to weakenings of common belief in rationality (CBR). We weaken ICR to ICR-lambda, being lambda a sequence whose kth component is the probability players attach to kth-order belief in rationality. The WY-discontinuity is found robust for constant lambda, and non-robust for lambda converging to 0. I.e., when CBR breaks down almost completely at high orders, the intuitive continuity of behavior with respect to perturbations of belief hierarchies is restored. ICR-lambda formalizes some well-known behavioral concepts (level-k and cognitive hierarchy models) in the language of classical game theory.

ABSTRACT. How can a researcher identify the number of levels of reasoning undertaken by players in a game? We focus on the case where the researcher cannot observe players' beliefs. Instead, the researcher has access to data which serve as a signal of the players' strategies. In the case of simultaneous-move games, standard results relate levels of reasoning to rounds of elimination of dominated strategies and, thereby, allow the researcher to partition the data to answer this question. However, in extensive-form games, levels of reasoning cannot be directly related to elimination of conditionally dominated strategies. The main theorem of this paper shows how to solve the researcher's inference problem in extensive-form games.

ABSTRACT. This talk has been cancelled.

ABSTRACT. In classical cooperative game theory it is assumed that any coalition of players may form. However, in many practical situations the set of feasible coalitions is limited by some social, economical, hierarchical, or technical structure. In this paper we assume that restrictions on cooperation are given by an arbitrary directed graph (digraph) on the player set, the directed links of which prescribe the subordination among the players. We introduce the Shapley value for digraph games that are TU games with limited cooperation determined by a digraph. It is defined as the average of the marginal contribution vectors corresponding to all permutations which do not violate the induced subordination of players. We study properties of this solution and its core stability. For digraph games with the digraphs being directed cycles an axiomatization of the solution is obtained.

ABSTRACT. In Briata, Dall'Aglio and Fragnelli (2012), the authors introduce a cooperative game with transferable utility for allocating the gain of a collusion among completely risk-averse agents involved in a fair division procedure introduced by Knaster (1946). In this paper we analyze the features of the Shapley value (Shapley, 1953) of the game, and propose a simple algorithm for computing it efficiently.

ABSTRACT. We investigate the effects of voting power in a committee in which one member (the chairman) holds, on top of a regular vote, also the power to break ties. In contrast to the equilibrium prediction under strategic voting, known as the Chairman’s Paradox, experimental data reveals that the tie-breaking power of the chairman is large and real. The chairman is able to induce her preferred outcome much more often than predicted, but only partially because of exercising tie-breaking power directly. The advantage of the chairman is largely determined by the limited strategic sophistication of committee members and the chairman’s salient position in the committee.

ABSTRACT. We consider a collective choice problem. A society needs to select a subset of a set of feasible alternatives over which each individual has a strict preference. We provide three axiomatic characterizations of a specific election method, plurality rule, which selects the alternative(s) most preferred by the largest number of individuals. Our first characterization strengthens the characterization result by Ching [Ching, S. (1996). A simple characterization of plurality rule. Journal of Economic Theory, 71(1):298-302] by replacing independence of dominated candidates by the weaker axiom called cloning-consistency. Our second result replaces the efficiency axiom of Yeh [Yeh, C.-H. (2008). An efficiency characterization of plurality rule in collective choice problems. Economic Theory, 34(3):575-583] by a weaker version of independence of irrelevant alternatives. Additionally, we provide a third, independent characterization using a weakened version of cloning-consistency.

ABSTRACT. We provide a characterization of the probability-weighted minimal norm solution for Bayesian social choice problems. This solution prescribes the incentive feasible utility allocation that minimizes a probability-weighted norm to an interim reference point. The solution is uniquely determined by four axioms: weak extension independence, interim Pareto optimality, symmetry for a class of transferable utility problems and interim symmetry by rescaling. We discuss the solution’s duality property and some illustrations.

ABSTRACT. We conducted two experiments showing that self-image concerns trump inequality aversion and help overcome fear of competition. We focused on performance curiosity, that is, the desire to know one’s own performance. Participants chose between an equal allocation and a performance-based, competitive one within a small group after generating surplus in a real-effort task. In the experimental treatment, avoiding competition by choosing an equal allocation came at the cost of not knowing the own performance, which led to a substantial increase of performance-based choices in comparison with the control treatment. The effect was especially pronounced for women, and the analysis reveals that the origin of this gender effect is a difference in expectations regarding performance.

ABSTRACT. Given the substantial evidence of behavioral heterogeneity in social dilemma experiments, in this study we consider how to achieve cooperation in n-player prisoner’s dilemma situations where each player has one behavioral type, either selfish or conditionally cooperative. We introduce a two-stage game form called the stay-leave mechanism, where each cooperator has the chance to revise his choice when players’ choices are not unanimous. For homogeneous behavioral type cases, theory predicts that the unique outcome is cooperative under the stay-leave mechanism. For heterogeneous behavioral type cases, selfish types tend to exploit conditionally cooperative types as the latter increases. The average cooperation rate in the stay-leave mechanism experiment is 86.6% across 15 periods, which increases to 96.0% after period 5. We also provide evidence that selfish and conditionally cooperative types coexist throughout the sessions. Our results corroborate the importance of incorporating behavioral heterogeneity into institutional design.

ABSTRACT. Before a group can take a decision, its members must agree on a mechanism to aggregate individual preferences. In this paper we present a first experimental test of the effect of participation constraints in such group choice situations. While efficient mechanisms are desirable, Myerson and Satterthwaite (1983) show that participation constraints can prevent their implementation. We experimentally show this effect in the context of social choice mechanisms for the provision of an indivisible public good. We find strong indications that individual preferences for choice rules are sensitive to individual expected payoffs. This highlights the importance of considering participation constraints when designing choice institutions. We contrast the empirical performance of the theoretically optimal mechanism (AGV) with the common Simple Majority voting mechanism (SM). Both do not achieve their theoretical efficiency. The SM is more robust to changes in the environment, but the AGV is more efficient in most treatments.

ABSTRACT. Vote-trading is common practice in committees and group decision-making. Yet we know very little about its properties. Inspired by the similarity between the logic of sequential rounds of pairwise vote-trading and matching algorithms, we explore three central questions that have parallels in the matching literature: (1) Does a stable allocation of votes always exists? (2) Is it reachable through a decentralized algorithm? (3) What welfare properties does it possess? We prove that a stable allocation exists and is always reached in a finite number of trades, for any number of voters and issues, for any separable preferences, and for any rule on how trades are prioritized. Its welfare properties however are guaranteed to be desirable only under specific conditions. A laboratory experiment confirms that stability has predictive power on the vote allocation achieved via sequential pairwise trades, but lends only weak support to the dynamic algorithm itself.

Joint work with Alessandra Casella.